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Effect of external stress on deuteride (hydride) precipitation in Zircaloy-4 using in situ neutron diffraction
Journal of Nuclear Materials 487 (2017) 396e405
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Journal of Nuclear Materials journal homepage: www.elsevier.com/locate/jnucmat
Effect of external stress on deuteride (hydride) precipitation in Zircaloy-4 using in situ neutron diffraction Jun-li Lin a, Ke An b, Alexandru D. Stoica b, Brent J. Heuser a, * a b
Department of Nuclear, Plasma, and Radiological Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA Chemical and Engineering Materials Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 30 August 2016 Received in revised form 22 December 2016 Accepted 25 January 2017 Available online 14 February 2017
In situ neutron diffraction is utilized to study the deuteride (hydride) precipitation behavior in a coldworked stress-relieved (CWSR) Zircaloy-4 material upon cooling from 420 C to room temperature with a 78 MPa external stress applied along the rolling direction (RD) of the material. Two banks detector capture the diffraction signal from two principal directions of the specimen, the normal direction (ND) and the rolling direction (RD). The evolution of deuterium concentration in zirconium solid solution along the two specimen directions is measured by studying the d-(220) peak intensity, applying the Rietveld refinement method to the diffraction data and using the measured zirconium c-axis lattice distortion. The deuterium concentration is observed to be higher for zirconium grains in the ND than the RD. The terminal solid solubility of precipitation (TSSp) for deuterium in the solution is then described using the Arrhenius equation. It is observed that the applied stress reduces the energy term Q in the Arrhenius equation when compared with the unstressed Q values from the work of others. A model by Puls is applied to study the effect of stress on deuterium solubility, with polycrystalline hydride precipitation strain calculated using the Kearns factor representative of the studied material. The experimental result does not agree with the model prediction of Puls. © 2017 Elsevier B.V. All rights reserved.
Keywords: Neutron diffraction Zirconium alloys Zirconium deuteride (hydride) Deuterium (hydrogen) solubility
1. Introduction Zircaloy is one of the most common fuel cladding materials used in light water reactors due to excellent mechanical properties, corrosion resistance, and low thermal neutron absorption crosssection. During operation, hydrogen is created by corrosion of outer wall of the cladding and radiolysis of the water coolant. A fraction of hydrogen diffuses into the cladding and is dissolved in the zirconium solid solution, and eventually precipitates out as zirconium hydrides when the hydrogen concentration exceeds the terminal solid solubility [1]. These hydrides distribute inhomogeneously within the cladding. The most typical observation of this inhomogeneity is the hydride rim (a near-surface layer contained high concentration of hydrides) and the hydride blister structure (a near-surface layer contained very high concentration of hydrides or bulky solid hydride phase) on the water-side of post-service cladding due to presence of the temperature gradient in the radial
* Corresponding author. E-mail address: [email protected] (B.J. Heuser). http://dx.doi.org/10.1016/j.jnucmat.2017.01.042 0022-3115/© 2017 Elsevier B.V. All rights reserved.
direction [2]. The hydrogen concentration in the rim structure can reach 1300 wppm while the average concentration of the cladding is approximate 400 wppm [3]. Besides the radial direction in the cladding, temperature gradients also exist in the axial and azimuthal directions during operation. This is caused by a combination effect of heat production in the fuel, local heat transfer condition, local oxide growth and heterogeneity of the core geometry. Regions of colder temperature such as inter-pellet gaps, corners, and side of assemblies have been observed to have higher hydride concentration [4,5]. This heterogeneous hydride distribution causes a significant loss of ductility of the cladding, while the brittle fracture characteristic of a hydride blister morphology has been observed occur at a very broad temperature range of 25e400 C [6]. Different local stress states in the components can also affect the hydride distribution. It is known that precipitation of the less dense hydride phase (d-hydride) will elastically and plastically distort the zirconium phase [7]. This plastic strain energy is compensated by undercooling required to precipitate the hydride upon cooling. Hence the precipitation temperature (temperature to start precipitating the hydride also known as TSSp) of zirconium hydride is
J.-l. Lin et al. / Journal of Nuclear Materials 487 (2017) 396e405
lower than the dissolution temperature (temperature to fully dissolve the hydride also known as TSSd), resulting in a hysteresis between the TSSd and TSSp solvi. In principal, the strain energy provided by an external tensile should reduce the hysteresis by decreasing the TSSd and increasing the TSSp solvus [8,9]. Understanding of the effect of stress on the hydrogen solubility and hydride precipitation behavior in the zirconium alloys is critical for the accurate prediction of the fuel performance, either during the service or in the post-service storage. For example, current delayed hydride cracking (DHC) model significantly relies on the hydride precipitation/dissolution behavior under a stressed state [10]. However, there are very limited experimental data that have studied the hydrogen solid solubility and the hydride precipitation under an applied load [11,12]. This work studies the dependence of hydrogen terminal solid solubility for precipitation (TSSp) on the external tensile stress utilizes the in situ time-of-flight (TOF) neutron diffraction, with two stationary banks that record two different grain orientation families. The effect of the tensile stress is examined by comparing the data in this work with other stress-free experimental results and the model prediction.
2. Experiment 2.1. Sample preparation Cold-worked stress-relieved (CWSR) Zircaloy-4 material with the thickness of 3 mm was provided by ATI Specialty Alloys and Components. This relative thick sample is used to increase the measured volume and the neutron diffraction signal. The basal pole figure of this material is shown in Fig. 1a. The typical basal plane orientation of the CWSR Zircaloy [1,13] is observed with the alignment of two basal poles tilted 30e40 from the normal direction (ND) and resides within the RD-TD plane. The chemical composition of the plate is consistent with ASTM Standards B35312 specification for Zircaloy-4 [14]. Dog-bone tensile specimens were machined using the electrical discharge machining (EDM) to avoid generating the machining residual stress. The dimension of this tensile specimen is specified in Fig. 1a alongside the basal pole figure showing the orientation of this tensile specimen. The surfaces of the tensile specimens were mechanically polished to 0.05 mm silica suspension. A thin film of Ni ( 0:2 mm was sputter coated on the polished surface to enhance the near-surface deuterium diffusion into the specimen [6,13]. The specimen was charged with deuterium using a Sievert-type apparatus gas system [15]. Deuterium is selected over hydrogen in this experiment due to its low neutron incoherent scattering cross section and large coherent scattering cross section. The deuterium charging was performed at 400 C under the stress-free condition in a vacuum (108 torr) environment. The variation of the deuterium partial pressure in the system is monitored by capacitance manometer gauges until the desired amount of deuterium concentration in the specimen has been reached [15]. The specimen was then slowly cooled (1 C min-1) to the room temperature to ensure that only the d-deuteride precipitated [16]. This gas charging method aims to create a thin layer of deuteride rim/blister near the surface of the specimen to simulate the hydride rim structure observed on the post-service cladding tubes. The microscopic examination in Fig. 1b from the ND-RD plane of the specimen shows a 20 mm near-surface deuteride rim/blister structure with an average deuterium concentration of 1054 wppm throughout the sample. This is consistent with the observation by Lin et al. [13] in terms of the hydrogen-equivalent concentration (527 wppm of hydrogen in this study versus 500 wppm of hydrogen in Ref. [13]).
397
2.2. Time-of-flight neutron diffraction and data analysis In situ time-of-flight (TOF) neutron diffraction experiment was conducted using the VULCAN engineering materials diffractometer at Spallation Neutron Source (SNS) at Oak Ridge National Laboratory [17]. The VULCAN-MTS load frame system and an induction coil were used for in situ mechanical and thermal testing. The sample was heated to 420 C, held for 1.5 h then cooled back to the room temperature at 1 C min-1 with a 78 MPa constant external tensile stress applied along the RD throughout the cooling process. TOF neutron diffraction spectra was continuously recorded throughout the experiment using the two stationary bank detectors sitting at the diffraction angles of ±90+ with ±11:5+ covered by each detector. The in situ experimental procedure and the arrangement are schematically shown in Fig. 1b and c. This study also demonstrates the ability of VULCAN to perform an in situ study on a minor phase in a bulk material, such as the zirconium deuteride phase in this work. The TOF neutron diffraction spectra were binned into 8 increments with each increment containing 60 min of the neutron exposure time. The temperature and stress magnitude of each increment are therefore an average value in the corresponding 60 min period. This relative long exposure time is necessary to obtain the statistically significant minor phase peaks from the zirconium deuteride. Data analysis (spectra integration and peak fitting) was performed using VULCAN Data Reduction and Interactive Visualization (VDRIVE) software to obtain the diffraction peak information for the two phases (a-Zr and d-deuteride), such as variation of the peak intensity and plane spacing throughout the in situ measurement. The binned spectra were first normalized to the incoherent vanadium diffraction spectra and the spallation source proton charge. The Debye-Waller factor and the change of zirconium matrix texture are expected to be negligible throughout the experiment [18]. Thus, it is plausible to assume that any change of the peak intensity is caused by the change of the amount of deuteride in the measured volume, and the volume fraction of the d-deuteride phase in the measured volume is linearly proportional to the measured integrated peak intensity [11,18]. Therefore, the calculation of the amount of deuterium in the d-deuteride phase can be based on the evolution of the d-(220) reflection intensity since this peak does not overlap with the strong zirconium peaks, as can be seen in Fig. 2a and b. The d-(220) thus provides the best single peak fit result for this study. Although the d-(311) has higher multiplicity factor (24) than the d-(220) reflection (12), the observed counting statistic is much worse than the d-(220) in this case. The integrated d-(220) peak intensity measured at 70 C is used as the reference when deuterium is fully precipitated. We note that the solubility of deuterium in the zirconium at 70 C is approximated 2 wppm [19], thus taking 70 C as the reference will slightly overestimate the amount of deuterium in the deuteride phase, but this deviation is negligible. Using the aforementioned linear relationship between the ddeuteride volume fraction and the measured integrated peak intensity, the evolution of the deuteride phase volume fraction throughout cooling can be expressed as: d Ið220Þ ðTÞ Vfd ðTÞ ¼ Vfd;0 d Ið220Þ;0
(1)
where Vfd ðTÞ is the volume fraction of the d-phase at temperature T, Vfd;0 is the volume fraction of the d-phase when deuteride is fully d d precipitated (the 70 C reference), Ið220Þ ðTÞ and Ið220Þ;0 are the measured integrated d-(220) peak intensity at the temperature T
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Fig. 1. (a) The dimension of the dog-bone tensile specimen with a basal pole figure shows the corresponding orientation of the specimen.(b) Experimental arrangement of VULCAN. Bank 1 and Bank 2 recorded the lattice planes with their normal parallel to scattering vector Q1 and Q2, respectively. Q1 and Q2 correspond to the RD and ND in terms of the sample orientation, respectively. The external load is applied along the RD, while the deuteride rim/blister is on the ND surface. The incident neutron beam is at 45 with respect to the ND/ TD. (c) The thermal and mechanical history throughout the in situ experiment, with the black solid line and the red dot-dash line represents the stress and the temperature value, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
and 70 C, respectively. The amount of deuterium in the Zircaloy solid solution is then determined by applying the conservation rule: +
½Da ðTÞ ¼
C d d ½D70 ave wf ðTÞ ½D ðTÞ
1 wf ðTÞd
(2)
where ½Da is the equilibrium amount of deuterium in the solid solution at the temperature T, wdf is the d-phase weight fraction and is simply the conversion of the measured Vfd in Eq. (1), using the density values of the two phases in [20]. ½Dd ðTÞ is the equilibrium deuterium concentration in the d-phase, which depends on the temperature T and is determined by the d-phase boundary 70+ C measured in the Zr-H binary phase diagram [21]. ½Dave is the deuterium concentration in the deuteride phase at 70 C. This value is expected to be different between two banks since deuteride precipitation strongly depends on Zr grain orientation. Thus,
+
70 C ½Dave , which can also be regarded as the deuteride phase fraction, for each bank is measured by performing the whole pattern Rietveld refinement on diffraction spectrum at 70 C using the GSAS software [22,23]. The strong texture of this material is refined using the spherical harmonics model, while the number of refined coefficients was carefully chosen to obtain a unique solution without losing the physical meaning. An example of the refined spectrum is shown in Fig. 2c. The whole pattern fitting yields another way to measure the deuterium concentration in the solid solution by using:
+
C d ½DaRF ðTÞ ¼ ½D70 ave ½DRF ðTÞ
(3)
½DdRF ðTÞ is the deuterium concentration in the d-deuteride phase at temperature T. Subscript RF indicates that this value is measured by the Rietveld fitting. Eqn. (3) simply accounts the decreased deuterium concentration in the deuteride phase as the amount of
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399
Fig. 2. Examples of partial neutron diffraction spectra from the (a) dð220Þ reflection and the (b) dð111Þ reflection. The red dash line represents the spectrum taken at 420 C while the black solid line was taken at 70 C. Also shown are examples of Rietveld refinement for diffraction spectrum at 70 C for (c) Bank 1 and (d) Bank 2. The subplot shows the residual of the fitting. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
deuterium dissolved into the zirconium matrix. ½DaRF ðTÞ thus represents the result that is sampled from all detected grains in each bank, while ½Da ðTÞ in Eqn. (2) only includes a subset of detected grains in each bank. 3. Results It is worth first to note that d is the only deuteride phase observed in this study, which is a common observation in CWSR Zry-4 material with a similar hydrogen-equivalent concentration and has precipitated hydride in a slow cooling rate (1 min-1) [24]. No reflections from other deuteride phases (g and ε) were observed. 70+ C The ½Dave value is measured as 660 and 1500 wppm deuterium for Bank 1 (RD) and Bank 2 (ND), respectively. We note that the different values between the RD and the ND is caused by the different texture detected in each bank, thus these values are
only true when considered for Zr grains with certain orientations that were detected under this experimental setup. The average 70+ C ½Dave value of two banks is very close to the bulk average value of the specimen, which is 1054 wppm deuterium. Fig. 3a shows the evolution of ½Da ðTÞ and ½DaRF ðTÞ, calculated by Eqns. (2) and (3), respectively. The result indicates that the evolution of ½Da and ½DaRF is comparable as shown in the figure. This confirms that under the experimental conditions of this work, using the intensity evolution of a single d(220) peak is sufficient to represent the precipitation behavior of the deuteride phase in each bank, although the single peak analysis only includes a subset of grains. Thus, the following discussion will only focus on the result of ½Da . ½Da ðTÞ can then be described using the Arrhenius equation to quantify the TSSp line, represented as hydrogen-equivalent concentration to be comparable with other literature values:
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Fig. 3. (a) Evolution of the deuterium concentration in the zirconium solid solution. Square and circle represents the ½DaRF and ½Da with red and black color represents the ND and the RD bank, respectively. The uncertainties are within the size of the data marker. A subplot shows the corresponding temperature and stress values at each data points. (b) Arrhenius fit of the ½Da (represented as hydrogen-equivalent concentration) in the zirconium solid solution. The square and circle makers represent the RD and the ND data, while the red dashed and the black solid line represents the RD and the ND fit, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
CTSSp ¼ AexpðQ =RTÞ
(4)
where CTSSp is the equilibrium deuterium solvus upon cooling. A is a pre-exponential constant and Q is an energy term which includes, in this case, the change of enthalpy for deuterium in solid solution, the strain energy to accommodate the precipitation of less dense deuteride and the work done by the external stress. The Arrhenius fit is shown in Fig. 3b uses the York linear regression method [25] which weights the uncertainty that is propagated from the
diffraction peak fitting, with the numerical values summarized in Table 1. The TSSp solvus in the two directions are listed for ½Da :
18400±1230 C½ND a ¼ 19150exp D RT
(5a)
20420±1440 C½RD ¼ 11700exp Da RT
(5b)
The superscripts of C denotes the corresponding direction.
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401
Table 1 Summary of the TSSp experimental conditions and results for hydride/deuteride in Zry-4 materials. Author
Technique
TOF, 23 span along ND on dð220Þ
ND This work C½D a
RD This work C½D a
TOF, 23 span along RD on dð220Þ
This work from caxis McMinn 2000 [26] Tang 2009 [27] Zanellato 2012 [18] Colas 2013 [11] Colas 2013 [11] Kim 2014 [28]
TOF, 23 span along ND, lattice distortion DSC DSC SXD, 20 span along TD on dð311Þ SXD, 20 span along TD on dð111Þ SXD, 20 span along TD on dð111Þ DSC
½Htot (wppm)
527 (Hequivalent) 527 (Hequivalent) 527 (Hequivalent) 20 to 80 20 to 240 475 to 600 190 to 350 190 to 350 40 to 731
Tmax ( C)
heating/cooling rate ( C/ min)
holding time (min)
sapplied
420
25/1
60
78 // RD
19150
18400 ± 1230
420
25/1
60
78 // RD
11700
20420 ± 1440
420
25/1
60
78 // RD
20570
19540 ± 1950
330 500 570 450 450 550
2/2 10/10 5/5 25/1 25/1 20/20
None 5 30 60 60 5
None None None 160 // TD None None
138746 40135 66440
34467.52 27336 29630 ± 160 12040 24320 26843
Previous studies have shown that the TSSd does not depend on thermal history but the TSSp for hydrogen in zirconium solid solution could be significantly affected by the thermal history [19]. Examples of the relevant thermal history are heating/cooling rate for dissolving/precipitating the deuteride (hydride), maximum temperature during the heating and holding period at the maximum temperature [26]. The composition (only minor difference exist between Zircaloy families) and the microstructure of the material has little effect on both the TSSd and the TSSp [26]. The TSS value is also different when studying different zirconium grain orientations [12]. Thus, a clear indication of measurement condition is necessary when comparing the TSSp value in this study with other work. Table 1 summarizes the experimentally measured TSSp solvus of our work and other studies under the stated experimental condition and technique. The value of the Q for precipitation found in this study are smaller than the value found in the literature for the unstressed material, both for studies which used the bulk-average method [26e28] and for studies which only included a subset of zirconium grains [11,18]. In this work with 78 MPa stress applied along the RD, Q is decreased by 4 kJ/mol. The work done by Colas et al. [11] with 160 MPa stress applied along the TD, Q was decreased by 12 kJ/ mol, although the authors attributed this change to the large uncertainty of their experiment. These results imply an inverse relationship between applied stress and the Q upon cooling. The theoretical model for the effect of the elastic stress on the equilibrium solvus of dissolved hydrogen in the metal solid solution was developed as [29]:
CH ¼
CH0 exp
V H sh RT
! (6)
where CHsh is the equilibrium hydrogen solvus for a measured vol0 is the equilibrium ume under a hydrostatic stress sh and CH hydrogen solvus for a region where the sh ¼ 0. V H is the partial molar volume of hydrogen in the metal. Eqn. (6) was further modified by Coleman and Ambler [30] by assuming the precipitation of hydride phase and the dissolved hydrogen were in equilibrium, the solvus then becomes:
sh
CH ¼
h V H V H sh
CH0 exp h
TSSp solvus A Q (J/mol) (wppm)
47220
precipitation of hydride. A similar equation was also developed by Puls [8,31]:
4. Discussion
sh
(MPa)
RT
(7)
where V H is the hydrogen partial molar volume associated with the
CHsh ¼ CH0 exp
a
W s V exp h H xRT RT
(8)
where x is the number of moles of hydrogen in a mole of hydride a ZrHx. The total molar accommodation energy W , is the energy associated with the accommodation of the hydride phase volume change in an external stress field sij and is given by a h W ¼ V H sij εT;hyd where εhyd is the stress-free strain associated ij ij with the transformation from the zirconium to the hydride phase. Carpenter [7] has estimated εhyd theoretically using the misfit between lattice cells of the two phases (d-hydride and a-Zr) with a specific orientation relationship of dð111Þ k að0001Þ in a single zirconium grain. The result was then further extended by Singh et al. [32] by including the temperature dependence for εhyd in a single zirconium grain, which is
εhyd ¼ 0:0371 þ 2:3111 105 T a
(9a)
¼ 0:06463 þ 1:9315 105 T εhyd c
(9b)
for the deformation along the a and c axis of a zirconium grain, respectively. T is the temperature in K. The εhyd value in a polycrystal sample along a principle direction i can then be represented using the formula [33]. hyd
εi
hyd
¼ f i εc
hyd
þ ð1 fi Þεa
(10)
where f is the Kearns factor. f was calculated using the basal pole figure of the tested material in this work (Fig. 1a) and the formula in Ref. [34], and is found to be equal to 0.65 in the ND, 0.27 in the TD and 0.07 in the RD. These values are in good agreement with values reported in Ref. [11] for a similar material. We then obtained the bulk εhyd values along the three principal directions of the specimen using Eqns. (9) and (10), which are
εRD ¼ 0:039 þ 2:2845 105 T
(11a)
εTD ¼ 0:0445 þ 2:2086 105 T
(11b)
5 εhyd ND ¼ 0:0549 þ 2:0644 10 T
(11c)
hyd
hyd
Puls's model (Eqn. (8)) can then be quantitatively evaluated with h the V H and V H value measured in Ref. [35] and the x obtained from
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the d-phase boundary line in the Zr-H phase diagram [21] to compare with the experimental measurement. Eqn. (8) can be simplified to sh CH ¼ CH0 exp
DQ RT
(12)
where DQ is the change of Q due to the externally applied stress. Q is increased or decreased when DQ > 0 or DQ < 0, respectively. From Eqn. (4) it is clear to see the increase of Q will decrease the solubility C, while the decrease of Q increases the C. Fig. 4 shows the DQ values predicted by Eqn. (8). Different stress magnitude applied along the different directions simulates the test conditions in this work and in Ref. [11], while the same stress values applied along the different directions is also calculated to compare the effect of the stress applied direction. The result shows the DQ is similar between the two applied directions with the same stress value. It is also observed that the externally applied stress decreases the Q at low temperature and increases the Q at high temperature, with the transition temperature at around 580e610 K, depends on the stress applied direction. However, this predicted change of Q is much smaller (with a difference in an order of 1 kJ/mol H) than what is observed in this experiment. In fact, in a work by Puls [36], Eqn. (8) was numerically evaluated at the crack tip area of a single zirconium grain which can be considered as an extreme case, since the hydrostatic stress at the tip can approach 1800 MPa. However, even at this high stress, the Q is only reduced by an order of 0.1 kJ/mol at 523 K. Thus, the model prediction is in disagreement with the observation of this work and [11], where the measured Q is greatly reduced when compared with unstressed Q values reported from other literature. Another method to measure the amount of hydrogen in the solid solution without reference to the diffraction-detected hydride fraction is to use the known dependency of the zirconium lattice
parameter on the amount of dissolved hydrogen. This was also done in Ref. [12]. The dilatation of the zirconium lattice parameter due to the hydrogen in the interstitial sites is anisotropic with the larger strain observed along the c-axis [35]. Thus, the c-axis strain is more sensitive to the variation of hydrogen concentration in the solid solution. The value of this dilatation was measured as 1 dc c0 dCD x2:427 mε per wppm of deuterium in the zirconium solid solution with the negligible temperature dependence [35]. The evolution of the zirconium c-axis strain throughout this experiment is calculated using the d-spacing of the að0002Þ basal plane. The thermal expansion strain [37] and the elastic strain [38] induced by the external stress on the c-axis is subtracted before we evaluated the strain induced by the deuterium in the solution. This analysis is only applicable in the ND (bank 2 detector in this case) since the að0002Þ peak was absent in the RD due to the texture of the studied material. The evolution of the c-axis lattice parameter as a function of temperature is shown in Fig. 5a along with the calculated thermal expansion value. Fig. 5b shows c-axis strain after subtraction of the thermal and the mechanical induced strain, while the corresponding deuterium concentration is shown in Fig. 5c. The Arrhenius equation is again applied to fit the deuterium concentration in the solution obtained using the c-axis strain. The fitted TSSp solvus, denoted with a superscript c-strain, is
19540±1950 CDcstrain; ND ¼ 20570exp RT
(13)
with the Q value close to Eqn. (5a). The TSSp solvus of Eqn. 5 and 13 and the data reported in Ref. [11] are shown together in Fig. 6 for comparison. The hydrogen-equivalent concentration measured by the c-axis deformation has lower solubility than calculated by Eqn. (2), with the largest difference measured as 280 wppm deuterium at 420 C.
Fig. 4. The change of Q due to the external applied tensile stress, predicted by Eqn. (8). The blue solid line, red dot-dash line, and the black dash line represents the result of a 78 MPa stress along the RD, a 160 MPa stress along the RD and a 160 MPa stress along the TD. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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403
Fig. 5. (a) The evolution of the c lattice parameter as the function of temperature in this study along with the predicted thermal expansion line displayed in a red dash line. (b) The strain on the c-axis after subtraction of the thermal and the mechanical strain. This represents only the strain induced by the interstitial deuterium. (c) The amount of deuterium in the matrix solid solution evaluated using the c-axis strain and Eqn. (2). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
This difference might be due to the different sampled subsets of zirconium grains between the two methods (using d-(220) peak and the c-axis distortion). However, this effect is negligible when the uncertainty is considered by a comparison of the two TSSp solvus (Eqn. (5)a and (13)). The two measured directions, RD and ND, correspond to the grain sets which were under the largest tensile strain and the largest concomitant Poisson compressive strain, respectively. The measured Q of the two directions is close to the same value (see Table 1), but grains detected in the ND have much higher deuterium concentration in the solid solution than grains in the RD. This is because the d-deuteride phase tends to preferentially precipitate in the ND section due to the stronger zirconium basal pole intensity in this direction. The larger tensile strain on grains in the RD did not cause redistribution and accumulation of deuteride phase. This might be due to the relatively small stress applied (78 MPa) in this study or the unfavorable stress applied direction for deuteride redistribution (RD versus TD). As also pointed out by Hardie [39], hydride reorientation is favored in grains with basal poles parallel to the direction of the applied stress, namely, grains in the ND and
the TD for the CWSR Zry-4 material. In other words, hydride reorientation will be difficult to occur in the grain set along the RD of the material. It is also observed in Fig. 6 that the TSSp solvus measured by Colas et al. [11] is lower than the result of this work. From Fig. 4 the effect of stress on Q is nearly independent of the applied direction. However, it should be noted that because of different subset grains sample (see Table 1) and the analysis method employed in the two studies, more work will be needed to resolve this difference.
5. Conclusion The work studies the effect of the external stress on the deuteride precipitation behavior in a CWSR Zry-4 material. The main observations are summarized below: 1 d-zirconium deuteride is the only deuteride phase observed in this study by neutron diffraction following an ex situ 1 C min-1 cooling procedure.
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Fig. 6. TSSp data measured in this work with the black circle, red square, and blue triangle represents the measurement from the d(220) peak along the RD and ND, and the measurement from the c-strain analysis, respectively. Also shown is data reported by Colas et al.[11], represented as the green reverse triangle. Data measured in this work has 78 MPa stress applied along the RD, while the data of Colas et al. has 160 MPa stress applied along the TD of the specimen. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
2 It is observed that between the RD and the ND directions the deuteride phase preferentially precipitates in Zr grains with their c-axis along the ND for a CWSR Zry-4 material. The deuteride weight fraction is measured as 1500 and 660 wppm deuterium along the ND and the RD, respectively, while the average total amount of deuterium in the specimen is 1054 wppm. 3 Adopting classic Arrhenius equation to describe the hydrogenequivalent solvus, the measured energy Q in both directions is smaller than the unstressed Q values reported in the literature. This is true when compared with studies which used the bulkaverage method and for studies which only included a subset of zirconium grains. The result implies the externally applied tensile stress reduces the Q value. This also suggests that the application of a 78 MPa tensile stress upon cooling increase the solubility of the material at the scale of individual grains. 4 Puls's model is numerically applied to study the effect of stress on Q, with temperature dependent polycrystalline hydride transformation strain calculated using the Kearns factor determined from the pole figure. The model predicted the external stress has negligible effect on Q, in disagreement with the experimental observation of this study. Acknowledgments The authors greatly appreciate access to the VULCAN instrument. The authors would also like to acknowledge M. Frost for his assistance with the neutron experimental work at VULCAN. This work was supported by the US Department of Energy Nuclear Energy Fuel Aging in Storage and Transportation under Grant No. IRP2011-05352, and by the US Department of Energy Nuclear Energy University Programs Integrated Research Project under contract number IRP-12-4728. The work was also carried out in part in the Frederick Seitz Materials Research Laboratory Central Research Facilities, University of Illinois. This research used resources at the
Spallation Neutron Source, a DOE Office of Science User Facility operated by the Oak Ridge National Laboratory. References [1] C. Lemaignan, A.T. Motta, in: R.W. Cahn, P. Haasen, E.J. Kramer (Eds.), Materials Science and Technology e A Comprehensive Treatment vol. 10B, 1994, p. 1 (Chapter 7). [2] A. Sawatzky, Can. Metall. Q. 24 (1985) 227e234. [3] P. Bossis, D. Pecheur, K. Hanifi, J. Thomazet, M. Blat, in: 14th International Symposium on Zirconium in the Nuclear Industry, volume 3, pp. 494e525. [4] A. M. Garde, S. R. Pati, M. A. Krammen, G. P. Smith, R. K. Endter, in: Zirconium in the Nuclear Industry: Tenth International Symposium, ASTM International. [5] O. Courty, A.T. Motta, J.D. Hales, J. Nucl. Mater. 452 (2014) 311e320. [6] O. Pierron, D. Koss, A. Motta, K. Chan, J. Nucl. Mater. 322 (2003) 21e35. [7] G. Carpenter, J. Nucl. Mater. 48 (1973) 264e266. [8] M. Puls, Acta Metall. 29 (1981) 1961e1968. [9] T.B. Flannagan, N. Mason, H. Birnbaum, The Effect of Stress on Hydride Precipitation., Technical Report, DTIC Document, 1980. [10] M. Puls, Metall. Trans. A 21 (1990) 2905e2917. [11] K.B. Colas, A.T. Motta, M.R. Daymond, J.D. Almer, J. Nucl. Mater. 440 (2013) 586e595. [12] P. Vizcaíno, J. Santisteban, M.V. Alvarez, A. Banchik, J. Almer, J. Nucl. Mater. 447 (2014) 82e93. [13] J.-l. Lin, X. Han, B.J. Heuser, J.D. Almer, J. Nucl. Mater. 471 (2016) 299e307. [14] ASTM standard B353-12, Specification for wrought zirconium and zirconium alloy seamless and welded tubes for nuclear service (except nuclear fuel cladding). www.astm.org, 2012. [15] W. Chen, B.J. Heuser, J. Alloys Compd. 312 (2000) 176e180. [16] J. Bradbrook, G. Lorimer, N. Ridley, J. Nucl. Mater. 42 (1972) 142e160. [17] X.-L. Wang, T. Holden, G.Q. Rennich, A. Stoica, P.K. Liaw, H. Choo, C.R. Hubbard, Phys. B Condens. Matter 385 (2006) 673e675. [18] O. Zanellato, M. Preuss, J.-Y. Buffiere, F. Ribeiro, A. Steuwer, J. Desquines, J. Andrieux, B. Krebs, J. Nucl. Mater. 420 (2012) 537e547. [19] Z. Pan, I. Ritchie, M. Puls, J. Nucl. Mater. 228 (1996) 227e237. [20] S. Yamanaka, K. Yamada, K. Kurosaki, M. Uno, K. Takeda, H. Anada, T. Matsuda, S. Kobayashi, J. Alloys Compd. 330 (2002) 99e104. [21] E. Zuzek, J. Abriata, A. San-Martin, F. Manchester, Bull. Alloy Phase Diagrams 11 (1990) 385e395. [22] A. Larson, R. Von Dreele, Los Alamos National Laboratory, Los Alamos, NM (1986). [23] B.H. Toby, J. Appl. Crystallogr. 34 (2001) 210e213. [24] R. Daum, Y. Chu, A. Motta, J. Nucl. Mater. 392 (2009) 453e463. [25] D. York, N.M. Evensen, M.L. Martınez, J.D.B. Delgado, Am. J. Phys. 72 (2004)
J.-l. Lin et al. / Journal of Nuclear Materials 487 (2017) 396e405 367e375. [26] A. McMinn, E. C. Darby, J. S. Schofield, in: Zirconium in the Nuclear Industry: Twelfth International Symposium, ASTM International. [27] R. Tang, X. Yang, Int. J. Hydrogen Energy 34 (2009) 7269e7274. [28] J.-S. Kim, Y.-S. Kim, Int. J. Hydrogen Energy 39 (2014) 16442e16449. [29] J. Li, R. Oriani, L. Darken, Z. für Phys. Chem. 49 (1966) 271e290. [30] C. Coleman, J. Ambler, Scr. Metall. 17 (1983) 77e82. [31] M. Puls, Acta Metall. 32 (1984) 1259e1269. [32] R.N. Singh, P. Ståhle, A.R. Massih, A. Shmakov, J. Alloys Compd. 436 (2007)
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150e154. [33] P. Tempest, J. Nucl. Mater. 92 (1980) 191e200. [34] A. Anderson, R. Thompson, C. Cook, Metallurgical Mater. Trans. A 30 (1999) 1981e1988. [35] S. MacEwen, C. Coleman, C. Ells, J. Faber, Acta Metall. 33 (1985) 753e757. [36] M.P. Puls, J. Nucl. Mater. 393 (2009) 350e367. [37] J. Goldak, L. Lloyd, C. Barrett, Phys. Rev. 144 (1966) 478. [38] E. Fisher, C. Renken, Phys. Rev. 135 (1964) A482. [39] D. Hardie, M. Shanahan, J. Nucl. Mater. 55 (1975) 1e13.
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Effect of external stress on deuteride (hydride) precipitation in Zircaloy-4 using in situ neutron diffraction Jun-li Lin a, Ke An b, Alexandru D. Stoica b, Brent J. Heuser a, * a b
Department of Nuclear, Plasma, and Radiological Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA Chemical and Engineering Materials Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 30 August 2016 Received in revised form 22 December 2016 Accepted 25 January 2017 Available online 14 February 2017
In situ neutron diffraction is utilized to study the deuteride (hydride) precipitation behavior in a coldworked stress-relieved (CWSR) Zircaloy-4 material upon cooling from 420 C to room temperature with a 78 MPa external stress applied along the rolling direction (RD) of the material. Two banks detector capture the diffraction signal from two principal directions of the specimen, the normal direction (ND) and the rolling direction (RD). The evolution of deuterium concentration in zirconium solid solution along the two specimen directions is measured by studying the d-(220) peak intensity, applying the Rietveld refinement method to the diffraction data and using the measured zirconium c-axis lattice distortion. The deuterium concentration is observed to be higher for zirconium grains in the ND than the RD. The terminal solid solubility of precipitation (TSSp) for deuterium in the solution is then described using the Arrhenius equation. It is observed that the applied stress reduces the energy term Q in the Arrhenius equation when compared with the unstressed Q values from the work of others. A model by Puls is applied to study the effect of stress on deuterium solubility, with polycrystalline hydride precipitation strain calculated using the Kearns factor representative of the studied material. The experimental result does not agree with the model prediction of Puls. © 2017 Elsevier B.V. All rights reserved.
Keywords: Neutron diffraction Zirconium alloys Zirconium deuteride (hydride) Deuterium (hydrogen) solubility
1. Introduction Zircaloy is one of the most common fuel cladding materials used in light water reactors due to excellent mechanical properties, corrosion resistance, and low thermal neutron absorption crosssection. During operation, hydrogen is created by corrosion of outer wall of the cladding and radiolysis of the water coolant. A fraction of hydrogen diffuses into the cladding and is dissolved in the zirconium solid solution, and eventually precipitates out as zirconium hydrides when the hydrogen concentration exceeds the terminal solid solubility [1]. These hydrides distribute inhomogeneously within the cladding. The most typical observation of this inhomogeneity is the hydride rim (a near-surface layer contained high concentration of hydrides) and the hydride blister structure (a near-surface layer contained very high concentration of hydrides or bulky solid hydride phase) on the water-side of post-service cladding due to presence of the temperature gradient in the radial
* Corresponding author. E-mail address: [email protected] (B.J. Heuser). http://dx.doi.org/10.1016/j.jnucmat.2017.01.042 0022-3115/© 2017 Elsevier B.V. All rights reserved.
direction [2]. The hydrogen concentration in the rim structure can reach 1300 wppm while the average concentration of the cladding is approximate 400 wppm [3]. Besides the radial direction in the cladding, temperature gradients also exist in the axial and azimuthal directions during operation. This is caused by a combination effect of heat production in the fuel, local heat transfer condition, local oxide growth and heterogeneity of the core geometry. Regions of colder temperature such as inter-pellet gaps, corners, and side of assemblies have been observed to have higher hydride concentration [4,5]. This heterogeneous hydride distribution causes a significant loss of ductility of the cladding, while the brittle fracture characteristic of a hydride blister morphology has been observed occur at a very broad temperature range of 25e400 C [6]. Different local stress states in the components can also affect the hydride distribution. It is known that precipitation of the less dense hydride phase (d-hydride) will elastically and plastically distort the zirconium phase [7]. This plastic strain energy is compensated by undercooling required to precipitate the hydride upon cooling. Hence the precipitation temperature (temperature to start precipitating the hydride also known as TSSp) of zirconium hydride is
J.-l. Lin et al. / Journal of Nuclear Materials 487 (2017) 396e405
lower than the dissolution temperature (temperature to fully dissolve the hydride also known as TSSd), resulting in a hysteresis between the TSSd and TSSp solvi. In principal, the strain energy provided by an external tensile should reduce the hysteresis by decreasing the TSSd and increasing the TSSp solvus [8,9]. Understanding of the effect of stress on the hydrogen solubility and hydride precipitation behavior in the zirconium alloys is critical for the accurate prediction of the fuel performance, either during the service or in the post-service storage. For example, current delayed hydride cracking (DHC) model significantly relies on the hydride precipitation/dissolution behavior under a stressed state [10]. However, there are very limited experimental data that have studied the hydrogen solid solubility and the hydride precipitation under an applied load [11,12]. This work studies the dependence of hydrogen terminal solid solubility for precipitation (TSSp) on the external tensile stress utilizes the in situ time-of-flight (TOF) neutron diffraction, with two stationary banks that record two different grain orientation families. The effect of the tensile stress is examined by comparing the data in this work with other stress-free experimental results and the model prediction.
2. Experiment 2.1. Sample preparation Cold-worked stress-relieved (CWSR) Zircaloy-4 material with the thickness of 3 mm was provided by ATI Specialty Alloys and Components. This relative thick sample is used to increase the measured volume and the neutron diffraction signal. The basal pole figure of this material is shown in Fig. 1a. The typical basal plane orientation of the CWSR Zircaloy [1,13] is observed with the alignment of two basal poles tilted 30e40 from the normal direction (ND) and resides within the RD-TD plane. The chemical composition of the plate is consistent with ASTM Standards B35312 specification for Zircaloy-4 [14]. Dog-bone tensile specimens were machined using the electrical discharge machining (EDM) to avoid generating the machining residual stress. The dimension of this tensile specimen is specified in Fig. 1a alongside the basal pole figure showing the orientation of this tensile specimen. The surfaces of the tensile specimens were mechanically polished to 0.05 mm silica suspension. A thin film of Ni ( 0:2 mm was sputter coated on the polished surface to enhance the near-surface deuterium diffusion into the specimen [6,13]. The specimen was charged with deuterium using a Sievert-type apparatus gas system [15]. Deuterium is selected over hydrogen in this experiment due to its low neutron incoherent scattering cross section and large coherent scattering cross section. The deuterium charging was performed at 400 C under the stress-free condition in a vacuum (108 torr) environment. The variation of the deuterium partial pressure in the system is monitored by capacitance manometer gauges until the desired amount of deuterium concentration in the specimen has been reached [15]. The specimen was then slowly cooled (1 C min-1) to the room temperature to ensure that only the d-deuteride precipitated [16]. This gas charging method aims to create a thin layer of deuteride rim/blister near the surface of the specimen to simulate the hydride rim structure observed on the post-service cladding tubes. The microscopic examination in Fig. 1b from the ND-RD plane of the specimen shows a 20 mm near-surface deuteride rim/blister structure with an average deuterium concentration of 1054 wppm throughout the sample. This is consistent with the observation by Lin et al. [13] in terms of the hydrogen-equivalent concentration (527 wppm of hydrogen in this study versus 500 wppm of hydrogen in Ref. [13]).
397
2.2. Time-of-flight neutron diffraction and data analysis In situ time-of-flight (TOF) neutron diffraction experiment was conducted using the VULCAN engineering materials diffractometer at Spallation Neutron Source (SNS) at Oak Ridge National Laboratory [17]. The VULCAN-MTS load frame system and an induction coil were used for in situ mechanical and thermal testing. The sample was heated to 420 C, held for 1.5 h then cooled back to the room temperature at 1 C min-1 with a 78 MPa constant external tensile stress applied along the RD throughout the cooling process. TOF neutron diffraction spectra was continuously recorded throughout the experiment using the two stationary bank detectors sitting at the diffraction angles of ±90+ with ±11:5+ covered by each detector. The in situ experimental procedure and the arrangement are schematically shown in Fig. 1b and c. This study also demonstrates the ability of VULCAN to perform an in situ study on a minor phase in a bulk material, such as the zirconium deuteride phase in this work. The TOF neutron diffraction spectra were binned into 8 increments with each increment containing 60 min of the neutron exposure time. The temperature and stress magnitude of each increment are therefore an average value in the corresponding 60 min period. This relative long exposure time is necessary to obtain the statistically significant minor phase peaks from the zirconium deuteride. Data analysis (spectra integration and peak fitting) was performed using VULCAN Data Reduction and Interactive Visualization (VDRIVE) software to obtain the diffraction peak information for the two phases (a-Zr and d-deuteride), such as variation of the peak intensity and plane spacing throughout the in situ measurement. The binned spectra were first normalized to the incoherent vanadium diffraction spectra and the spallation source proton charge. The Debye-Waller factor and the change of zirconium matrix texture are expected to be negligible throughout the experiment [18]. Thus, it is plausible to assume that any change of the peak intensity is caused by the change of the amount of deuteride in the measured volume, and the volume fraction of the d-deuteride phase in the measured volume is linearly proportional to the measured integrated peak intensity [11,18]. Therefore, the calculation of the amount of deuterium in the d-deuteride phase can be based on the evolution of the d-(220) reflection intensity since this peak does not overlap with the strong zirconium peaks, as can be seen in Fig. 2a and b. The d-(220) thus provides the best single peak fit result for this study. Although the d-(311) has higher multiplicity factor (24) than the d-(220) reflection (12), the observed counting statistic is much worse than the d-(220) in this case. The integrated d-(220) peak intensity measured at 70 C is used as the reference when deuterium is fully precipitated. We note that the solubility of deuterium in the zirconium at 70 C is approximated 2 wppm [19], thus taking 70 C as the reference will slightly overestimate the amount of deuterium in the deuteride phase, but this deviation is negligible. Using the aforementioned linear relationship between the ddeuteride volume fraction and the measured integrated peak intensity, the evolution of the deuteride phase volume fraction throughout cooling can be expressed as: d Ið220Þ ðTÞ Vfd ðTÞ ¼ Vfd;0 d Ið220Þ;0
(1)
where Vfd ðTÞ is the volume fraction of the d-phase at temperature T, Vfd;0 is the volume fraction of the d-phase when deuteride is fully d d precipitated (the 70 C reference), Ið220Þ ðTÞ and Ið220Þ;0 are the measured integrated d-(220) peak intensity at the temperature T
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Fig. 1. (a) The dimension of the dog-bone tensile specimen with a basal pole figure shows the corresponding orientation of the specimen.(b) Experimental arrangement of VULCAN. Bank 1 and Bank 2 recorded the lattice planes with their normal parallel to scattering vector Q1 and Q2, respectively. Q1 and Q2 correspond to the RD and ND in terms of the sample orientation, respectively. The external load is applied along the RD, while the deuteride rim/blister is on the ND surface. The incident neutron beam is at 45 with respect to the ND/ TD. (c) The thermal and mechanical history throughout the in situ experiment, with the black solid line and the red dot-dash line represents the stress and the temperature value, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
and 70 C, respectively. The amount of deuterium in the Zircaloy solid solution is then determined by applying the conservation rule: +
½Da ðTÞ ¼
C d d ½D70 ave wf ðTÞ ½D ðTÞ
1 wf ðTÞd
(2)
where ½Da is the equilibrium amount of deuterium in the solid solution at the temperature T, wdf is the d-phase weight fraction and is simply the conversion of the measured Vfd in Eq. (1), using the density values of the two phases in [20]. ½Dd ðTÞ is the equilibrium deuterium concentration in the d-phase, which depends on the temperature T and is determined by the d-phase boundary 70+ C measured in the Zr-H binary phase diagram [21]. ½Dave is the deuterium concentration in the deuteride phase at 70 C. This value is expected to be different between two banks since deuteride precipitation strongly depends on Zr grain orientation. Thus,
+
70 C ½Dave , which can also be regarded as the deuteride phase fraction, for each bank is measured by performing the whole pattern Rietveld refinement on diffraction spectrum at 70 C using the GSAS software [22,23]. The strong texture of this material is refined using the spherical harmonics model, while the number of refined coefficients was carefully chosen to obtain a unique solution without losing the physical meaning. An example of the refined spectrum is shown in Fig. 2c. The whole pattern fitting yields another way to measure the deuterium concentration in the solid solution by using:
+
C d ½DaRF ðTÞ ¼ ½D70 ave ½DRF ðTÞ
(3)
½DdRF ðTÞ is the deuterium concentration in the d-deuteride phase at temperature T. Subscript RF indicates that this value is measured by the Rietveld fitting. Eqn. (3) simply accounts the decreased deuterium concentration in the deuteride phase as the amount of
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399
Fig. 2. Examples of partial neutron diffraction spectra from the (a) dð220Þ reflection and the (b) dð111Þ reflection. The red dash line represents the spectrum taken at 420 C while the black solid line was taken at 70 C. Also shown are examples of Rietveld refinement for diffraction spectrum at 70 C for (c) Bank 1 and (d) Bank 2. The subplot shows the residual of the fitting. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
deuterium dissolved into the zirconium matrix. ½DaRF ðTÞ thus represents the result that is sampled from all detected grains in each bank, while ½Da ðTÞ in Eqn. (2) only includes a subset of detected grains in each bank. 3. Results It is worth first to note that d is the only deuteride phase observed in this study, which is a common observation in CWSR Zry-4 material with a similar hydrogen-equivalent concentration and has precipitated hydride in a slow cooling rate (1 min-1) [24]. No reflections from other deuteride phases (g and ε) were observed. 70+ C The ½Dave value is measured as 660 and 1500 wppm deuterium for Bank 1 (RD) and Bank 2 (ND), respectively. We note that the different values between the RD and the ND is caused by the different texture detected in each bank, thus these values are
only true when considered for Zr grains with certain orientations that were detected under this experimental setup. The average 70+ C ½Dave value of two banks is very close to the bulk average value of the specimen, which is 1054 wppm deuterium. Fig. 3a shows the evolution of ½Da ðTÞ and ½DaRF ðTÞ, calculated by Eqns. (2) and (3), respectively. The result indicates that the evolution of ½Da and ½DaRF is comparable as shown in the figure. This confirms that under the experimental conditions of this work, using the intensity evolution of a single d(220) peak is sufficient to represent the precipitation behavior of the deuteride phase in each bank, although the single peak analysis only includes a subset of grains. Thus, the following discussion will only focus on the result of ½Da . ½Da ðTÞ can then be described using the Arrhenius equation to quantify the TSSp line, represented as hydrogen-equivalent concentration to be comparable with other literature values:
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J.-l. Lin et al. / Journal of Nuclear Materials 487 (2017) 396e405
Fig. 3. (a) Evolution of the deuterium concentration in the zirconium solid solution. Square and circle represents the ½DaRF and ½Da with red and black color represents the ND and the RD bank, respectively. The uncertainties are within the size of the data marker. A subplot shows the corresponding temperature and stress values at each data points. (b) Arrhenius fit of the ½Da (represented as hydrogen-equivalent concentration) in the zirconium solid solution. The square and circle makers represent the RD and the ND data, while the red dashed and the black solid line represents the RD and the ND fit, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
CTSSp ¼ AexpðQ =RTÞ
(4)
where CTSSp is the equilibrium deuterium solvus upon cooling. A is a pre-exponential constant and Q is an energy term which includes, in this case, the change of enthalpy for deuterium in solid solution, the strain energy to accommodate the precipitation of less dense deuteride and the work done by the external stress. The Arrhenius fit is shown in Fig. 3b uses the York linear regression method [25] which weights the uncertainty that is propagated from the
diffraction peak fitting, with the numerical values summarized in Table 1. The TSSp solvus in the two directions are listed for ½Da :
18400±1230 C½ND a ¼ 19150exp D RT
(5a)
20420±1440 C½RD ¼ 11700exp Da RT
(5b)
The superscripts of C denotes the corresponding direction.
J.-l. Lin et al. / Journal of Nuclear Materials 487 (2017) 396e405
401
Table 1 Summary of the TSSp experimental conditions and results for hydride/deuteride in Zry-4 materials. Author
Technique
TOF, 23 span along ND on dð220Þ
ND This work C½D a
RD This work C½D a
TOF, 23 span along RD on dð220Þ
This work from caxis McMinn 2000 [26] Tang 2009 [27] Zanellato 2012 [18] Colas 2013 [11] Colas 2013 [11] Kim 2014 [28]
TOF, 23 span along ND, lattice distortion DSC DSC SXD, 20 span along TD on dð311Þ SXD, 20 span along TD on dð111Þ SXD, 20 span along TD on dð111Þ DSC
½Htot (wppm)
527 (Hequivalent) 527 (Hequivalent) 527 (Hequivalent) 20 to 80 20 to 240 475 to 600 190 to 350 190 to 350 40 to 731
Tmax ( C)
heating/cooling rate ( C/ min)
holding time (min)
sapplied
420
25/1
60
78 // RD
19150
18400 ± 1230
420
25/1
60
78 // RD
11700
20420 ± 1440
420
25/1
60
78 // RD
20570
19540 ± 1950
330 500 570 450 450 550
2/2 10/10 5/5 25/1 25/1 20/20
None 5 30 60 60 5
None None None 160 // TD None None
138746 40135 66440
34467.52 27336 29630 ± 160 12040 24320 26843
Previous studies have shown that the TSSd does not depend on thermal history but the TSSp for hydrogen in zirconium solid solution could be significantly affected by the thermal history [19]. Examples of the relevant thermal history are heating/cooling rate for dissolving/precipitating the deuteride (hydride), maximum temperature during the heating and holding period at the maximum temperature [26]. The composition (only minor difference exist between Zircaloy families) and the microstructure of the material has little effect on both the TSSd and the TSSp [26]. The TSS value is also different when studying different zirconium grain orientations [12]. Thus, a clear indication of measurement condition is necessary when comparing the TSSp value in this study with other work. Table 1 summarizes the experimentally measured TSSp solvus of our work and other studies under the stated experimental condition and technique. The value of the Q for precipitation found in this study are smaller than the value found in the literature for the unstressed material, both for studies which used the bulk-average method [26e28] and for studies which only included a subset of zirconium grains [11,18]. In this work with 78 MPa stress applied along the RD, Q is decreased by 4 kJ/mol. The work done by Colas et al. [11] with 160 MPa stress applied along the TD, Q was decreased by 12 kJ/ mol, although the authors attributed this change to the large uncertainty of their experiment. These results imply an inverse relationship between applied stress and the Q upon cooling. The theoretical model for the effect of the elastic stress on the equilibrium solvus of dissolved hydrogen in the metal solid solution was developed as [29]:
CH ¼
CH0 exp
V H sh RT
! (6)
where CHsh is the equilibrium hydrogen solvus for a measured vol0 is the equilibrium ume under a hydrostatic stress sh and CH hydrogen solvus for a region where the sh ¼ 0. V H is the partial molar volume of hydrogen in the metal. Eqn. (6) was further modified by Coleman and Ambler [30] by assuming the precipitation of hydride phase and the dissolved hydrogen were in equilibrium, the solvus then becomes:
sh
CH ¼
h V H V H sh
CH0 exp h
TSSp solvus A Q (J/mol) (wppm)
47220
precipitation of hydride. A similar equation was also developed by Puls [8,31]:
4. Discussion
sh
(MPa)
RT
(7)
where V H is the hydrogen partial molar volume associated with the
CHsh ¼ CH0 exp
a
W s V exp h H xRT RT
(8)
where x is the number of moles of hydrogen in a mole of hydride a ZrHx. The total molar accommodation energy W , is the energy associated with the accommodation of the hydride phase volume change in an external stress field sij and is given by a h W ¼ V H sij εT;hyd where εhyd is the stress-free strain associated ij ij with the transformation from the zirconium to the hydride phase. Carpenter [7] has estimated εhyd theoretically using the misfit between lattice cells of the two phases (d-hydride and a-Zr) with a specific orientation relationship of dð111Þ k að0001Þ in a single zirconium grain. The result was then further extended by Singh et al. [32] by including the temperature dependence for εhyd in a single zirconium grain, which is
εhyd ¼ 0:0371 þ 2:3111 105 T a
(9a)
¼ 0:06463 þ 1:9315 105 T εhyd c
(9b)
for the deformation along the a and c axis of a zirconium grain, respectively. T is the temperature in K. The εhyd value in a polycrystal sample along a principle direction i can then be represented using the formula [33]. hyd
εi
hyd
¼ f i εc
hyd
þ ð1 fi Þεa
(10)
where f is the Kearns factor. f was calculated using the basal pole figure of the tested material in this work (Fig. 1a) and the formula in Ref. [34], and is found to be equal to 0.65 in the ND, 0.27 in the TD and 0.07 in the RD. These values are in good agreement with values reported in Ref. [11] for a similar material. We then obtained the bulk εhyd values along the three principal directions of the specimen using Eqns. (9) and (10), which are
εRD ¼ 0:039 þ 2:2845 105 T
(11a)
εTD ¼ 0:0445 þ 2:2086 105 T
(11b)
5 εhyd ND ¼ 0:0549 þ 2:0644 10 T
(11c)
hyd
hyd
Puls's model (Eqn. (8)) can then be quantitatively evaluated with h the V H and V H value measured in Ref. [35] and the x obtained from
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the d-phase boundary line in the Zr-H phase diagram [21] to compare with the experimental measurement. Eqn. (8) can be simplified to sh CH ¼ CH0 exp
DQ RT
(12)
where DQ is the change of Q due to the externally applied stress. Q is increased or decreased when DQ > 0 or DQ < 0, respectively. From Eqn. (4) it is clear to see the increase of Q will decrease the solubility C, while the decrease of Q increases the C. Fig. 4 shows the DQ values predicted by Eqn. (8). Different stress magnitude applied along the different directions simulates the test conditions in this work and in Ref. [11], while the same stress values applied along the different directions is also calculated to compare the effect of the stress applied direction. The result shows the DQ is similar between the two applied directions with the same stress value. It is also observed that the externally applied stress decreases the Q at low temperature and increases the Q at high temperature, with the transition temperature at around 580e610 K, depends on the stress applied direction. However, this predicted change of Q is much smaller (with a difference in an order of 1 kJ/mol H) than what is observed in this experiment. In fact, in a work by Puls [36], Eqn. (8) was numerically evaluated at the crack tip area of a single zirconium grain which can be considered as an extreme case, since the hydrostatic stress at the tip can approach 1800 MPa. However, even at this high stress, the Q is only reduced by an order of 0.1 kJ/mol at 523 K. Thus, the model prediction is in disagreement with the observation of this work and [11], where the measured Q is greatly reduced when compared with unstressed Q values reported from other literature. Another method to measure the amount of hydrogen in the solid solution without reference to the diffraction-detected hydride fraction is to use the known dependency of the zirconium lattice
parameter on the amount of dissolved hydrogen. This was also done in Ref. [12]. The dilatation of the zirconium lattice parameter due to the hydrogen in the interstitial sites is anisotropic with the larger strain observed along the c-axis [35]. Thus, the c-axis strain is more sensitive to the variation of hydrogen concentration in the solid solution. The value of this dilatation was measured as 1 dc c0 dCD x2:427 mε per wppm of deuterium in the zirconium solid solution with the negligible temperature dependence [35]. The evolution of the zirconium c-axis strain throughout this experiment is calculated using the d-spacing of the að0002Þ basal plane. The thermal expansion strain [37] and the elastic strain [38] induced by the external stress on the c-axis is subtracted before we evaluated the strain induced by the deuterium in the solution. This analysis is only applicable in the ND (bank 2 detector in this case) since the að0002Þ peak was absent in the RD due to the texture of the studied material. The evolution of the c-axis lattice parameter as a function of temperature is shown in Fig. 5a along with the calculated thermal expansion value. Fig. 5b shows c-axis strain after subtraction of the thermal and the mechanical induced strain, while the corresponding deuterium concentration is shown in Fig. 5c. The Arrhenius equation is again applied to fit the deuterium concentration in the solution obtained using the c-axis strain. The fitted TSSp solvus, denoted with a superscript c-strain, is
19540±1950 CDcstrain; ND ¼ 20570exp RT
(13)
with the Q value close to Eqn. (5a). The TSSp solvus of Eqn. 5 and 13 and the data reported in Ref. [11] are shown together in Fig. 6 for comparison. The hydrogen-equivalent concentration measured by the c-axis deformation has lower solubility than calculated by Eqn. (2), with the largest difference measured as 280 wppm deuterium at 420 C.
Fig. 4. The change of Q due to the external applied tensile stress, predicted by Eqn. (8). The blue solid line, red dot-dash line, and the black dash line represents the result of a 78 MPa stress along the RD, a 160 MPa stress along the RD and a 160 MPa stress along the TD. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Fig. 5. (a) The evolution of the c lattice parameter as the function of temperature in this study along with the predicted thermal expansion line displayed in a red dash line. (b) The strain on the c-axis after subtraction of the thermal and the mechanical strain. This represents only the strain induced by the interstitial deuterium. (c) The amount of deuterium in the matrix solid solution evaluated using the c-axis strain and Eqn. (2). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
This difference might be due to the different sampled subsets of zirconium grains between the two methods (using d-(220) peak and the c-axis distortion). However, this effect is negligible when the uncertainty is considered by a comparison of the two TSSp solvus (Eqn. (5)a and (13)). The two measured directions, RD and ND, correspond to the grain sets which were under the largest tensile strain and the largest concomitant Poisson compressive strain, respectively. The measured Q of the two directions is close to the same value (see Table 1), but grains detected in the ND have much higher deuterium concentration in the solid solution than grains in the RD. This is because the d-deuteride phase tends to preferentially precipitate in the ND section due to the stronger zirconium basal pole intensity in this direction. The larger tensile strain on grains in the RD did not cause redistribution and accumulation of deuteride phase. This might be due to the relatively small stress applied (78 MPa) in this study or the unfavorable stress applied direction for deuteride redistribution (RD versus TD). As also pointed out by Hardie [39], hydride reorientation is favored in grains with basal poles parallel to the direction of the applied stress, namely, grains in the ND and
the TD for the CWSR Zry-4 material. In other words, hydride reorientation will be difficult to occur in the grain set along the RD of the material. It is also observed in Fig. 6 that the TSSp solvus measured by Colas et al. [11] is lower than the result of this work. From Fig. 4 the effect of stress on Q is nearly independent of the applied direction. However, it should be noted that because of different subset grains sample (see Table 1) and the analysis method employed in the two studies, more work will be needed to resolve this difference.
5. Conclusion The work studies the effect of the external stress on the deuteride precipitation behavior in a CWSR Zry-4 material. The main observations are summarized below: 1 d-zirconium deuteride is the only deuteride phase observed in this study by neutron diffraction following an ex situ 1 C min-1 cooling procedure.
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Fig. 6. TSSp data measured in this work with the black circle, red square, and blue triangle represents the measurement from the d(220) peak along the RD and ND, and the measurement from the c-strain analysis, respectively. Also shown is data reported by Colas et al.[11], represented as the green reverse triangle. Data measured in this work has 78 MPa stress applied along the RD, while the data of Colas et al. has 160 MPa stress applied along the TD of the specimen. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
2 It is observed that between the RD and the ND directions the deuteride phase preferentially precipitates in Zr grains with their c-axis along the ND for a CWSR Zry-4 material. The deuteride weight fraction is measured as 1500 and 660 wppm deuterium along the ND and the RD, respectively, while the average total amount of deuterium in the specimen is 1054 wppm. 3 Adopting classic Arrhenius equation to describe the hydrogenequivalent solvus, the measured energy Q in both directions is smaller than the unstressed Q values reported in the literature. This is true when compared with studies which used the bulkaverage method and for studies which only included a subset of zirconium grains. The result implies the externally applied tensile stress reduces the Q value. This also suggests that the application of a 78 MPa tensile stress upon cooling increase the solubility of the material at the scale of individual grains. 4 Puls's model is numerically applied to study the effect of stress on Q, with temperature dependent polycrystalline hydride transformation strain calculated using the Kearns factor determined from the pole figure. The model predicted the external stress has negligible effect on Q, in disagreement with the experimental observation of this study. Acknowledgments The authors greatly appreciate access to the VULCAN instrument. The authors would also like to acknowledge M. Frost for his assistance with the neutron experimental work at VULCAN. This work was supported by the US Department of Energy Nuclear Energy Fuel Aging in Storage and Transportation under Grant No. IRP2011-05352, and by the US Department of Energy Nuclear Energy University Programs Integrated Research Project under contract number IRP-12-4728. The work was also carried out in part in the Frederick Seitz Materials Research Laboratory Central Research Facilities, University of Illinois. This research used resources at the
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